Integral dari $$$s \sin{\left(10 x \right)}$$$ terhadap $$$x$$$

Temukan $$$\int s \sin{\left(10 x \right)}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=s$$$ dan $$$f{\left(x \right)} = \sin{\left(10 x \right)}$$$:

$${\color{red}{\int{s \sin{\left(10 x \right)} d x}}} = {\color{red}{s \int{\sin{\left(10 x \right)} d x}}}$$

Misalkan $$$u=10 x$$$.

Kemudian $$$du=\left(10 x\right)^{\prime }dx = 10 dx$$$ (langkah-langkah dapat dilihat di »), dan kita memperoleh $$$dx = \frac{du}{10}$$$.

Oleh karena itu,

$$s {\color{red}{\int{\sin{\left(10 x \right)} d x}}} = s {\color{red}{\int{\frac{\sin{\left(u \right)}}{10} d u}}}$$

Terapkan aturan pengali konstanta $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ dengan $$$c=\frac{1}{10}$$$ dan $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:

$$s {\color{red}{\int{\frac{\sin{\left(u \right)}}{10} d u}}} = s {\color{red}{\left(\frac{\int{\sin{\left(u \right)} d u}}{10}\right)}}$$

Integral dari sinus adalah $$$\int{\sin{\left(u \right)} d u} = - \cos{\left(u \right)}$$$:

$$\frac{s {\color{red}{\int{\sin{\left(u \right)} d u}}}}{10} = \frac{s {\color{red}{\left(- \cos{\left(u \right)}\right)}}}{10}$$

Ingat bahwa $$$u=10 x$$$:

$$- \frac{s \cos{\left({\color{red}{u}} \right)}}{10} = - \frac{s \cos{\left({\color{red}{\left(10 x\right)}} \right)}}{10}$$

Oleh karena itu,

$$\int{s \sin{\left(10 x \right)} d x} = - \frac{s \cos{\left(10 x \right)}}{10}$$

Tambahkan konstanta integrasi:

$$\int{s \sin{\left(10 x \right)} d x} = - \frac{s \cos{\left(10 x \right)}}{10}+C$$

$$$\int s \sin{\left(10 x \right)}\, dx = - \frac{s \cos{\left(10 x \right)}}{10} + C$$$A